The English Book of Mormon uses the term “Christian” four times. See Alma 46:13, 15, 16 & Alma 48:10. (There is also a reference to Christian Whitmer, a nineteenth century witness to the Book of Mormon plates.) This usage is well and good for English speakers.
A challenge is that “Christian” is derived from the Greek word “Christos” which means “anointed one.” The ancient Book of Mormon people were almost certainly unfamiliar with Greek. Rather they spoke Hebrew, or a modified version of Hebrew. They wrote in reformed Egyptian. Instead of a phonetic term for “Christian,” they would have probably used the equivalent Hebrew title “follower of the Messiah.” (לַתַּלְמִידִים מְשִׁיחִיִּים)
I need to verify the pronunciation of this title, but “The Messiah” is “HaMashiach.”
– Tom Irvine